where \(\Gamma _{\mathcal {H}}^{\rm SM}\)  denotes the total decay widths of the SM-like Higgs boson with mass being set to \(m_{\mathcal {H}}\) , and \(\Gamma _{\mathcal {H}\rightarrow XX}\)  is the width of \(\mathcal {H}\)  decaying to a pair of \(X\)  (\(=\chi , {\cal H}\) ), which can be found in appendix .
We see that the signal strengths of \(\mathcal {H}\)  is suppressed by two factors: \(\cos ^2\theta \) 
and the presence of new decay channels. Even when the new decay channels are kinematically forbidden, the signal strength is still reduced by \(\cos ^2\theta \) .
This means that a generic signature of the mixing of the SM Higgs boson with an extra singlet scalar boson can be derived from a reduced signal of the Higgs bosons at the LHC [1]}.
